PPT - Differential Calculus | Quantitative Aptitude for CA Foundation PDF Download

 Page 1


  Basic Concept of                                    
Differential and Integral Calculus 
 
CPT Section D Quantitative Aptitude Chapter 9 
Dr. Atul Kumar Srivastava 
 
Page 2


  Basic Concept of                                    
Differential and Integral Calculus 
 
CPT Section D Quantitative Aptitude Chapter 9 
Dr. Atul Kumar Srivastava 
 
Learning Objectives 
 
Understand the use of this Branch of mathematics in various branches of science 
and Humanities 
Understand the basics of differentiation and integration  
Know how to compute derivative of a function by the first principal, derivative 
of a function by the use of various formulae and higher order differentiation 
Make familiar with various techniques of integration  
Understand the concept of definite integrals of functions and its properties.  
2 
Page 3


  Basic Concept of                                    
Differential and Integral Calculus 
 
CPT Section D Quantitative Aptitude Chapter 9 
Dr. Atul Kumar Srivastava 
 
Learning Objectives 
 
Understand the use of this Branch of mathematics in various branches of science 
and Humanities 
Understand the basics of differentiation and integration  
Know how to compute derivative of a function by the first principal, derivative 
of a function by the use of various formulae and higher order differentiation 
Make familiar with various techniques of integration  
Understand the concept of definite integrals of functions and its properties.  
2 
Differential calculus-Outlines 
 
What is Differential Calculus – An Introduction  
Derivative or Deferential Coefficient (First Principal Definition)  
Basic Formulas 
Laws for Differentiation (Algebra of Derivative of Functions) 
Derivative of A Function of Function (Chain Rule) 
.Derivative of Implicit Function 
.Derivative of Function In Parametric Form  
3 
Page 4


  Basic Concept of                                    
Differential and Integral Calculus 
 
CPT Section D Quantitative Aptitude Chapter 9 
Dr. Atul Kumar Srivastava 
 
Learning Objectives 
 
Understand the use of this Branch of mathematics in various branches of science 
and Humanities 
Understand the basics of differentiation and integration  
Know how to compute derivative of a function by the first principal, derivative 
of a function by the use of various formulae and higher order differentiation 
Make familiar with various techniques of integration  
Understand the concept of definite integrals of functions and its properties.  
2 
Differential calculus-Outlines 
 
What is Differential Calculus – An Introduction  
Derivative or Deferential Coefficient (First Principal Definition)  
Basic Formulas 
Laws for Differentiation (Algebra of Derivative of Functions) 
Derivative of A Function of Function (Chain Rule) 
.Derivative of Implicit Function 
.Derivative of Function In Parametric Form  
3 
What is differential calculus – an 
introduction 
 
One of the most fundamental operations in calculus is that of differentiation. In 
the study of mathematics, there are many problems containing two quantities 
such that the value of one quantity depends upon the other. A variation in the 
value of any ones produces a variation in the value of the other. For example 
the area of a square depends upon it's side. The area of circle and volume of 
sphere depend upon their radius etc.  
Differential calculus is the Branch of Mathematics which studies changes 
To express the rate of change of any function we introduce concept of 
derivative. The concept involves a very small change in the dependent variable 
with reference to a very small change in the independent variable 
4 
Page 5


  Basic Concept of                                    
Differential and Integral Calculus 
 
CPT Section D Quantitative Aptitude Chapter 9 
Dr. Atul Kumar Srivastava 
 
Learning Objectives 
 
Understand the use of this Branch of mathematics in various branches of science 
and Humanities 
Understand the basics of differentiation and integration  
Know how to compute derivative of a function by the first principal, derivative 
of a function by the use of various formulae and higher order differentiation 
Make familiar with various techniques of integration  
Understand the concept of definite integrals of functions and its properties.  
2 
Differential calculus-Outlines 
 
What is Differential Calculus – An Introduction  
Derivative or Deferential Coefficient (First Principal Definition)  
Basic Formulas 
Laws for Differentiation (Algebra of Derivative of Functions) 
Derivative of A Function of Function (Chain Rule) 
.Derivative of Implicit Function 
.Derivative of Function In Parametric Form  
3 
What is differential calculus – an 
introduction 
 
One of the most fundamental operations in calculus is that of differentiation. In 
the study of mathematics, there are many problems containing two quantities 
such that the value of one quantity depends upon the other. A variation in the 
value of any ones produces a variation in the value of the other. For example 
the area of a square depends upon it's side. The area of circle and volume of 
sphere depend upon their radius etc.  
Differential calculus is the Branch of Mathematics which studies changes 
To express the rate of change of any function we introduce concept of 
derivative. The concept involves a very small change in the dependent variable 
with reference to a very small change in the independent variable 
4 
Continued  
 
                               y=f(x)   
•                                           x -   Independent variable  
•                                           y -   Dependent Variable  
Thus differentiation is a process of finding the derivative of a 
continuous function. It is defined as the limiting value of the 
ratio of the change in the function corresponding to small 
change in the independent variable as the later tends to zero.  
5